Solve (3x^2y^-3)^-2/x^-5y

$$\frac { ( 3 x ^ { 2 } y ^ { - 3 } ) ^ { - 2 } } { x ^ { - 5 } y }$$

Evaluate

$$\frac{xy^{5}}{9}$$

Solution Steps

Expand \left(3x^{2}y^{-3}\right)^{-2}.

$$\frac{3^{-2}\left(x^{2}\right)^{-2}\left(y^{-3}\right)^{-2}}{x^{-5}y}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{3^{-2}x^{-4}\left(y^{-3}\right)^{-2}}{x^{-5}y}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -2 to get 6.

$$\frac{3^{-2}x^{-4}y^{6}}{x^{-5}y}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{-4}y^{6}}{x^{-5}y}$$

Cancel out y in both numerator and denominator.

$$\frac{\frac{1}{9}x^{-4}y^{5}}{x^{-5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{1}{9}x^{1}y^{5}$$

Calculate x to the power of 1 and get x.

$$\frac{1}{9}xy^{5}$$

Expand

$$\frac{xy^{5}}{9}$$

Solution Steps

Expand \left(3x^{2}y^{-3}\right)^{-2}.

$$\frac{3^{-2}\left(x^{2}\right)^{-2}\left(y^{-3}\right)^{-2}}{x^{-5}y}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{3^{-2}x^{-4}\left(y^{-3}\right)^{-2}}{x^{-5}y}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -2 to get 6.

$$\frac{3^{-2}x^{-4}y^{6}}{x^{-5}y}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{-4}y^{6}}{x^{-5}y}$$

Cancel out y in both numerator and denominator.

$$\frac{\frac{1}{9}x^{-4}y^{5}}{x^{-5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{1}{9}x^{1}y^{5}$$

Calculate x to the power of 1 and get x.

$$\frac{1}{9}xy^{5}$$